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arXiv 1911.03087math.CO
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$1$ -几乎柏拉图图的不存在性

Absence of $1$-Nearly Platonic Graphs

Mahdi Reza Khorsandi, Seyed Reza Musawi

备注：
After we posted v1 on arXiv, D. Froncek and J. Qiu informed us that they had obtained independently the same results (although the proofs are organized differently). We decided to merge the papers into one. Since duplicate posting on arXiv is impossible, we refer the reader for our joint paper and any update to arXiv:1911.05135
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摘要：

一个$t$ -近似柏拉图图是一个有限的、连通的、正则的、简单的可平面图，其中除了恰好$t$个数之外，所有的面都具有相同的长度。证明了不存在2-连通$1$ -近柏拉图图。本文证明了不存在$1$ -近柏拉图图。

英文摘要：

A $t$-nearly platonic graph is a finite, connected, regular, simple and planar graph in which all but exactly $t$ numbers of its faces have the same length. It is proved that there is no 2-connected $1$-nearly platonic graph. In this paper, we prove that there is no $1$-nearly platonic graph.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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